Answer
$$\frac{-3}{10-\sqrt{6}}=\frac{-30-3\sqrt{6}}{94}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-3}{10-\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-3}{10-\sqrt{6}}\frac{10+\sqrt{6}}{10+\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-30-3\sqrt{6}}{100+10\sqrt{6}-10\sqrt{6}-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-30-3\sqrt{6}}{94}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 10 + \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -3 } \cdot \left( 10 + \sqrt{6}\right) = \color{blue}{-3} \cdot10\color{blue}{-3} \cdot \sqrt{6} = \\ = -30- 3 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 10- \sqrt{6}\right) } \cdot \left( 10 + \sqrt{6}\right) = \color{blue}{10} \cdot10+\color{blue}{10} \cdot \sqrt{6}\color{blue}{- \sqrt{6}} \cdot10\color{blue}{- \sqrt{6}} \cdot \sqrt{6} = \\ = 100 + 10 \sqrt{6}- 10 \sqrt{6}-6 $$ |
| ③ | Simplify numerator and denominator |
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